I am new to wordpress, Here i use the wordpress TwentyEleven theme, i need to customize the widget markup. It means the suppose i want to change the element 'ul' to div and add some class or id to this element. Now currently it was not possible for me because the wordpress default widgets are already available inside wordpress core file..

Just go to you widget administration page inside you wordpress interface and add an empty text widget to display this empty (invisible) widget instead (or any other widget if you want to display other widgets). Remember to accept my answer if it helps you solve your problem :)
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Ole Henrik SkogstrømJan 10 '12 at 13:01